Properties

Label 8020.2.a.c.1.4
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32143 q^{3}\) \(-1.00000 q^{5}\) \(+0.515797 q^{7}\) \(+2.38904 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32143 q^{3}\) \(-1.00000 q^{5}\) \(+0.515797 q^{7}\) \(+2.38904 q^{9}\) \(+4.54079 q^{11}\) \(+1.42147 q^{13}\) \(+2.32143 q^{15}\) \(+3.21357 q^{17}\) \(-2.56977 q^{19}\) \(-1.19739 q^{21}\) \(-0.925577 q^{23}\) \(+1.00000 q^{25}\) \(+1.41829 q^{27}\) \(-1.44774 q^{29}\) \(-6.16275 q^{31}\) \(-10.5411 q^{33}\) \(-0.515797 q^{35}\) \(-5.88040 q^{37}\) \(-3.29984 q^{39}\) \(-9.02106 q^{41}\) \(-7.54662 q^{43}\) \(-2.38904 q^{45}\) \(-1.06959 q^{47}\) \(-6.73395 q^{49}\) \(-7.46009 q^{51}\) \(+3.39722 q^{53}\) \(-4.54079 q^{55}\) \(+5.96555 q^{57}\) \(+8.53271 q^{59}\) \(+4.29821 q^{61}\) \(+1.23226 q^{63}\) \(-1.42147 q^{65}\) \(-7.75453 q^{67}\) \(+2.14866 q^{69}\) \(+7.31767 q^{71}\) \(+6.48265 q^{73}\) \(-2.32143 q^{75}\) \(+2.34213 q^{77}\) \(+6.18911 q^{79}\) \(-10.4596 q^{81}\) \(+16.0002 q^{83}\) \(-3.21357 q^{85}\) \(+3.36084 q^{87}\) \(+13.5007 q^{89}\) \(+0.733188 q^{91}\) \(+14.3064 q^{93}\) \(+2.56977 q^{95}\) \(+7.67511 q^{97}\) \(+10.8482 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.32143 −1.34028 −0.670140 0.742235i \(-0.733766\pi\)
−0.670140 + 0.742235i \(0.733766\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.515797 0.194953 0.0974765 0.995238i \(-0.468923\pi\)
0.0974765 + 0.995238i \(0.468923\pi\)
\(8\) 0 0
\(9\) 2.38904 0.796348
\(10\) 0 0
\(11\) 4.54079 1.36910 0.684550 0.728966i \(-0.259999\pi\)
0.684550 + 0.728966i \(0.259999\pi\)
\(12\) 0 0
\(13\) 1.42147 0.394244 0.197122 0.980379i \(-0.436841\pi\)
0.197122 + 0.980379i \(0.436841\pi\)
\(14\) 0 0
\(15\) 2.32143 0.599391
\(16\) 0 0
\(17\) 3.21357 0.779406 0.389703 0.920941i \(-0.372578\pi\)
0.389703 + 0.920941i \(0.372578\pi\)
\(18\) 0 0
\(19\) −2.56977 −0.589546 −0.294773 0.955567i \(-0.595244\pi\)
−0.294773 + 0.955567i \(0.595244\pi\)
\(20\) 0 0
\(21\) −1.19739 −0.261291
\(22\) 0 0
\(23\) −0.925577 −0.192996 −0.0964981 0.995333i \(-0.530764\pi\)
−0.0964981 + 0.995333i \(0.530764\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.41829 0.272950
\(28\) 0 0
\(29\) −1.44774 −0.268839 −0.134420 0.990925i \(-0.542917\pi\)
−0.134420 + 0.990925i \(0.542917\pi\)
\(30\) 0 0
\(31\) −6.16275 −1.10686 −0.553431 0.832895i \(-0.686682\pi\)
−0.553431 + 0.832895i \(0.686682\pi\)
\(32\) 0 0
\(33\) −10.5411 −1.83498
\(34\) 0 0
\(35\) −0.515797 −0.0871856
\(36\) 0 0
\(37\) −5.88040 −0.966732 −0.483366 0.875418i \(-0.660586\pi\)
−0.483366 + 0.875418i \(0.660586\pi\)
\(38\) 0 0
\(39\) −3.29984 −0.528397
\(40\) 0 0
\(41\) −9.02106 −1.40885 −0.704426 0.709777i \(-0.748796\pi\)
−0.704426 + 0.709777i \(0.748796\pi\)
\(42\) 0 0
\(43\) −7.54662 −1.15085 −0.575424 0.817855i \(-0.695163\pi\)
−0.575424 + 0.817855i \(0.695163\pi\)
\(44\) 0 0
\(45\) −2.38904 −0.356138
\(46\) 0 0
\(47\) −1.06959 −0.156016 −0.0780082 0.996953i \(-0.524856\pi\)
−0.0780082 + 0.996953i \(0.524856\pi\)
\(48\) 0 0
\(49\) −6.73395 −0.961993
\(50\) 0 0
\(51\) −7.46009 −1.04462
\(52\) 0 0
\(53\) 3.39722 0.466644 0.233322 0.972400i \(-0.425040\pi\)
0.233322 + 0.972400i \(0.425040\pi\)
\(54\) 0 0
\(55\) −4.54079 −0.612280
\(56\) 0 0
\(57\) 5.96555 0.790156
\(58\) 0 0
\(59\) 8.53271 1.11086 0.555432 0.831562i \(-0.312553\pi\)
0.555432 + 0.831562i \(0.312553\pi\)
\(60\) 0 0
\(61\) 4.29821 0.550330 0.275165 0.961397i \(-0.411268\pi\)
0.275165 + 0.961397i \(0.411268\pi\)
\(62\) 0 0
\(63\) 1.23226 0.155250
\(64\) 0 0
\(65\) −1.42147 −0.176311
\(66\) 0 0
\(67\) −7.75453 −0.947367 −0.473683 0.880695i \(-0.657076\pi\)
−0.473683 + 0.880695i \(0.657076\pi\)
\(68\) 0 0
\(69\) 2.14866 0.258669
\(70\) 0 0
\(71\) 7.31767 0.868448 0.434224 0.900805i \(-0.357023\pi\)
0.434224 + 0.900805i \(0.357023\pi\)
\(72\) 0 0
\(73\) 6.48265 0.758737 0.379368 0.925246i \(-0.376141\pi\)
0.379368 + 0.925246i \(0.376141\pi\)
\(74\) 0 0
\(75\) −2.32143 −0.268056
\(76\) 0 0
\(77\) 2.34213 0.266910
\(78\) 0 0
\(79\) 6.18911 0.696330 0.348165 0.937433i \(-0.386805\pi\)
0.348165 + 0.937433i \(0.386805\pi\)
\(80\) 0 0
\(81\) −10.4596 −1.16218
\(82\) 0 0
\(83\) 16.0002 1.75625 0.878125 0.478432i \(-0.158795\pi\)
0.878125 + 0.478432i \(0.158795\pi\)
\(84\) 0 0
\(85\) −3.21357 −0.348561
\(86\) 0 0
\(87\) 3.36084 0.360319
\(88\) 0 0
\(89\) 13.5007 1.43108 0.715538 0.698574i \(-0.246182\pi\)
0.715538 + 0.698574i \(0.246182\pi\)
\(90\) 0 0
\(91\) 0.733188 0.0768590
\(92\) 0 0
\(93\) 14.3064 1.48350
\(94\) 0 0
\(95\) 2.56977 0.263653
\(96\) 0 0
\(97\) 7.67511 0.779289 0.389645 0.920965i \(-0.372598\pi\)
0.389645 + 0.920965i \(0.372598\pi\)
\(98\) 0 0
\(99\) 10.8482 1.09028
\(100\) 0 0
\(101\) −15.5710 −1.54938 −0.774688 0.632343i \(-0.782093\pi\)
−0.774688 + 0.632343i \(0.782093\pi\)
\(102\) 0 0
\(103\) −3.28758 −0.323934 −0.161967 0.986796i \(-0.551784\pi\)
−0.161967 + 0.986796i \(0.551784\pi\)
\(104\) 0 0
\(105\) 1.19739 0.116853
\(106\) 0 0
\(107\) 3.65515 0.353357 0.176678 0.984269i \(-0.443465\pi\)
0.176678 + 0.984269i \(0.443465\pi\)
\(108\) 0 0
\(109\) −0.780421 −0.0747507 −0.0373754 0.999301i \(-0.511900\pi\)
−0.0373754 + 0.999301i \(0.511900\pi\)
\(110\) 0 0
\(111\) 13.6509 1.29569
\(112\) 0 0
\(113\) −3.57304 −0.336123 −0.168062 0.985777i \(-0.553751\pi\)
−0.168062 + 0.985777i \(0.553751\pi\)
\(114\) 0 0
\(115\) 0.925577 0.0863105
\(116\) 0 0
\(117\) 3.39595 0.313955
\(118\) 0 0
\(119\) 1.65755 0.151948
\(120\) 0 0
\(121\) 9.61879 0.874435
\(122\) 0 0
\(123\) 20.9418 1.88826
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.3561 1.45136 0.725682 0.688030i \(-0.241524\pi\)
0.725682 + 0.688030i \(0.241524\pi\)
\(128\) 0 0
\(129\) 17.5190 1.54246
\(130\) 0 0
\(131\) −17.7380 −1.54978 −0.774889 0.632098i \(-0.782194\pi\)
−0.774889 + 0.632098i \(0.782194\pi\)
\(132\) 0 0
\(133\) −1.32548 −0.114934
\(134\) 0 0
\(135\) −1.41829 −0.122067
\(136\) 0 0
\(137\) −13.2460 −1.13168 −0.565839 0.824516i \(-0.691448\pi\)
−0.565839 + 0.824516i \(0.691448\pi\)
\(138\) 0 0
\(139\) −7.27964 −0.617451 −0.308726 0.951151i \(-0.599902\pi\)
−0.308726 + 0.951151i \(0.599902\pi\)
\(140\) 0 0
\(141\) 2.48299 0.209106
\(142\) 0 0
\(143\) 6.45458 0.539759
\(144\) 0 0
\(145\) 1.44774 0.120229
\(146\) 0 0
\(147\) 15.6324 1.28934
\(148\) 0 0
\(149\) 14.1910 1.16257 0.581287 0.813699i \(-0.302549\pi\)
0.581287 + 0.813699i \(0.302549\pi\)
\(150\) 0 0
\(151\) −11.8909 −0.967664 −0.483832 0.875161i \(-0.660755\pi\)
−0.483832 + 0.875161i \(0.660755\pi\)
\(152\) 0 0
\(153\) 7.67737 0.620678
\(154\) 0 0
\(155\) 6.16275 0.495004
\(156\) 0 0
\(157\) −0.709493 −0.0566237 −0.0283118 0.999599i \(-0.509013\pi\)
−0.0283118 + 0.999599i \(0.509013\pi\)
\(158\) 0 0
\(159\) −7.88642 −0.625433
\(160\) 0 0
\(161\) −0.477410 −0.0376252
\(162\) 0 0
\(163\) −17.2640 −1.35222 −0.676112 0.736799i \(-0.736336\pi\)
−0.676112 + 0.736799i \(0.736336\pi\)
\(164\) 0 0
\(165\) 10.5411 0.820626
\(166\) 0 0
\(167\) 8.82603 0.682978 0.341489 0.939886i \(-0.389069\pi\)
0.341489 + 0.939886i \(0.389069\pi\)
\(168\) 0 0
\(169\) −10.9794 −0.844572
\(170\) 0 0
\(171\) −6.13930 −0.469484
\(172\) 0 0
\(173\) 0.823790 0.0626316 0.0313158 0.999510i \(-0.490030\pi\)
0.0313158 + 0.999510i \(0.490030\pi\)
\(174\) 0 0
\(175\) 0.515797 0.0389906
\(176\) 0 0
\(177\) −19.8081 −1.48887
\(178\) 0 0
\(179\) −0.190010 −0.0142020 −0.00710100 0.999975i \(-0.502260\pi\)
−0.00710100 + 0.999975i \(0.502260\pi\)
\(180\) 0 0
\(181\) −14.5591 −1.08217 −0.541083 0.840969i \(-0.681986\pi\)
−0.541083 + 0.840969i \(0.681986\pi\)
\(182\) 0 0
\(183\) −9.97801 −0.737596
\(184\) 0 0
\(185\) 5.88040 0.432336
\(186\) 0 0
\(187\) 14.5922 1.06708
\(188\) 0 0
\(189\) 0.731551 0.0532125
\(190\) 0 0
\(191\) −21.9084 −1.58523 −0.792617 0.609720i \(-0.791282\pi\)
−0.792617 + 0.609720i \(0.791282\pi\)
\(192\) 0 0
\(193\) −6.18409 −0.445140 −0.222570 0.974917i \(-0.571445\pi\)
−0.222570 + 0.974917i \(0.571445\pi\)
\(194\) 0 0
\(195\) 3.29984 0.236306
\(196\) 0 0
\(197\) −17.4254 −1.24151 −0.620756 0.784004i \(-0.713174\pi\)
−0.620756 + 0.784004i \(0.713174\pi\)
\(198\) 0 0
\(199\) −14.2398 −1.00943 −0.504717 0.863285i \(-0.668403\pi\)
−0.504717 + 0.863285i \(0.668403\pi\)
\(200\) 0 0
\(201\) 18.0016 1.26974
\(202\) 0 0
\(203\) −0.746742 −0.0524110
\(204\) 0 0
\(205\) 9.02106 0.630058
\(206\) 0 0
\(207\) −2.21125 −0.153692
\(208\) 0 0
\(209\) −11.6688 −0.807148
\(210\) 0 0
\(211\) 21.9263 1.50947 0.754734 0.656031i \(-0.227766\pi\)
0.754734 + 0.656031i \(0.227766\pi\)
\(212\) 0 0
\(213\) −16.9875 −1.16396
\(214\) 0 0
\(215\) 7.54662 0.514675
\(216\) 0 0
\(217\) −3.17873 −0.215786
\(218\) 0 0
\(219\) −15.0490 −1.01692
\(220\) 0 0
\(221\) 4.56798 0.307276
\(222\) 0 0
\(223\) 7.60831 0.509490 0.254745 0.967008i \(-0.418008\pi\)
0.254745 + 0.967008i \(0.418008\pi\)
\(224\) 0 0
\(225\) 2.38904 0.159270
\(226\) 0 0
\(227\) −0.536195 −0.0355885 −0.0177943 0.999842i \(-0.505664\pi\)
−0.0177943 + 0.999842i \(0.505664\pi\)
\(228\) 0 0
\(229\) 16.1704 1.06857 0.534286 0.845304i \(-0.320581\pi\)
0.534286 + 0.845304i \(0.320581\pi\)
\(230\) 0 0
\(231\) −5.43709 −0.357734
\(232\) 0 0
\(233\) 9.59466 0.628567 0.314284 0.949329i \(-0.398236\pi\)
0.314284 + 0.949329i \(0.398236\pi\)
\(234\) 0 0
\(235\) 1.06959 0.0697727
\(236\) 0 0
\(237\) −14.3676 −0.933276
\(238\) 0 0
\(239\) 25.1698 1.62810 0.814048 0.580798i \(-0.197259\pi\)
0.814048 + 0.580798i \(0.197259\pi\)
\(240\) 0 0
\(241\) −11.4350 −0.736591 −0.368295 0.929709i \(-0.620058\pi\)
−0.368295 + 0.929709i \(0.620058\pi\)
\(242\) 0 0
\(243\) 20.0264 1.28469
\(244\) 0 0
\(245\) 6.73395 0.430216
\(246\) 0 0
\(247\) −3.65284 −0.232425
\(248\) 0 0
\(249\) −37.1434 −2.35386
\(250\) 0 0
\(251\) −11.0793 −0.699322 −0.349661 0.936876i \(-0.613703\pi\)
−0.349661 + 0.936876i \(0.613703\pi\)
\(252\) 0 0
\(253\) −4.20285 −0.264231
\(254\) 0 0
\(255\) 7.46009 0.467169
\(256\) 0 0
\(257\) −9.82315 −0.612751 −0.306376 0.951911i \(-0.599116\pi\)
−0.306376 + 0.951911i \(0.599116\pi\)
\(258\) 0 0
\(259\) −3.03309 −0.188467
\(260\) 0 0
\(261\) −3.45872 −0.214090
\(262\) 0 0
\(263\) 9.01282 0.555754 0.277877 0.960617i \(-0.410369\pi\)
0.277877 + 0.960617i \(0.410369\pi\)
\(264\) 0 0
\(265\) −3.39722 −0.208690
\(266\) 0 0
\(267\) −31.3410 −1.91804
\(268\) 0 0
\(269\) −31.4219 −1.91583 −0.957914 0.287055i \(-0.907324\pi\)
−0.957914 + 0.287055i \(0.907324\pi\)
\(270\) 0 0
\(271\) −10.7742 −0.654484 −0.327242 0.944941i \(-0.606119\pi\)
−0.327242 + 0.944941i \(0.606119\pi\)
\(272\) 0 0
\(273\) −1.70205 −0.103013
\(274\) 0 0
\(275\) 4.54079 0.273820
\(276\) 0 0
\(277\) 30.6572 1.84202 0.921008 0.389544i \(-0.127367\pi\)
0.921008 + 0.389544i \(0.127367\pi\)
\(278\) 0 0
\(279\) −14.7231 −0.881448
\(280\) 0 0
\(281\) −9.39866 −0.560677 −0.280339 0.959901i \(-0.590447\pi\)
−0.280339 + 0.959901i \(0.590447\pi\)
\(282\) 0 0
\(283\) 18.4967 1.09951 0.549757 0.835325i \(-0.314720\pi\)
0.549757 + 0.835325i \(0.314720\pi\)
\(284\) 0 0
\(285\) −5.96555 −0.353369
\(286\) 0 0
\(287\) −4.65304 −0.274660
\(288\) 0 0
\(289\) −6.67295 −0.392527
\(290\) 0 0
\(291\) −17.8172 −1.04446
\(292\) 0 0
\(293\) −10.3951 −0.607288 −0.303644 0.952786i \(-0.598203\pi\)
−0.303644 + 0.952786i \(0.598203\pi\)
\(294\) 0 0
\(295\) −8.53271 −0.496794
\(296\) 0 0
\(297\) 6.44017 0.373696
\(298\) 0 0
\(299\) −1.31568 −0.0760876
\(300\) 0 0
\(301\) −3.89253 −0.224361
\(302\) 0 0
\(303\) 36.1471 2.07660
\(304\) 0 0
\(305\) −4.29821 −0.246115
\(306\) 0 0
\(307\) 21.6878 1.23779 0.618894 0.785474i \(-0.287581\pi\)
0.618894 + 0.785474i \(0.287581\pi\)
\(308\) 0 0
\(309\) 7.63188 0.434163
\(310\) 0 0
\(311\) 15.7859 0.895134 0.447567 0.894250i \(-0.352291\pi\)
0.447567 + 0.894250i \(0.352291\pi\)
\(312\) 0 0
\(313\) 13.9086 0.786160 0.393080 0.919504i \(-0.371410\pi\)
0.393080 + 0.919504i \(0.371410\pi\)
\(314\) 0 0
\(315\) −1.23226 −0.0694301
\(316\) 0 0
\(317\) −4.52800 −0.254318 −0.127159 0.991882i \(-0.540586\pi\)
−0.127159 + 0.991882i \(0.540586\pi\)
\(318\) 0 0
\(319\) −6.57390 −0.368068
\(320\) 0 0
\(321\) −8.48519 −0.473597
\(322\) 0 0
\(323\) −8.25815 −0.459496
\(324\) 0 0
\(325\) 1.42147 0.0788488
\(326\) 0 0
\(327\) 1.81169 0.100187
\(328\) 0 0
\(329\) −0.551694 −0.0304159
\(330\) 0 0
\(331\) −28.9864 −1.59324 −0.796618 0.604483i \(-0.793380\pi\)
−0.796618 + 0.604483i \(0.793380\pi\)
\(332\) 0 0
\(333\) −14.0485 −0.769855
\(334\) 0 0
\(335\) 7.75453 0.423675
\(336\) 0 0
\(337\) −4.05627 −0.220959 −0.110480 0.993878i \(-0.535239\pi\)
−0.110480 + 0.993878i \(0.535239\pi\)
\(338\) 0 0
\(339\) 8.29456 0.450499
\(340\) 0 0
\(341\) −27.9838 −1.51541
\(342\) 0 0
\(343\) −7.08393 −0.382497
\(344\) 0 0
\(345\) −2.14866 −0.115680
\(346\) 0 0
\(347\) 16.8017 0.901960 0.450980 0.892534i \(-0.351075\pi\)
0.450980 + 0.892534i \(0.351075\pi\)
\(348\) 0 0
\(349\) 13.4514 0.720037 0.360018 0.932945i \(-0.382770\pi\)
0.360018 + 0.932945i \(0.382770\pi\)
\(350\) 0 0
\(351\) 2.01605 0.107609
\(352\) 0 0
\(353\) −21.1803 −1.12731 −0.563656 0.826010i \(-0.690606\pi\)
−0.563656 + 0.826010i \(0.690606\pi\)
\(354\) 0 0
\(355\) −7.31767 −0.388382
\(356\) 0 0
\(357\) −3.84789 −0.203652
\(358\) 0 0
\(359\) −14.2466 −0.751905 −0.375953 0.926639i \(-0.622684\pi\)
−0.375953 + 0.926639i \(0.622684\pi\)
\(360\) 0 0
\(361\) −12.3963 −0.652435
\(362\) 0 0
\(363\) −22.3294 −1.17199
\(364\) 0 0
\(365\) −6.48265 −0.339317
\(366\) 0 0
\(367\) 2.98613 0.155874 0.0779372 0.996958i \(-0.475167\pi\)
0.0779372 + 0.996958i \(0.475167\pi\)
\(368\) 0 0
\(369\) −21.5517 −1.12194
\(370\) 0 0
\(371\) 1.75228 0.0909737
\(372\) 0 0
\(373\) −14.7039 −0.761341 −0.380671 0.924711i \(-0.624307\pi\)
−0.380671 + 0.924711i \(0.624307\pi\)
\(374\) 0 0
\(375\) 2.32143 0.119878
\(376\) 0 0
\(377\) −2.05792 −0.105988
\(378\) 0 0
\(379\) 30.3896 1.56101 0.780503 0.625151i \(-0.214963\pi\)
0.780503 + 0.625151i \(0.214963\pi\)
\(380\) 0 0
\(381\) −37.9695 −1.94523
\(382\) 0 0
\(383\) −30.0848 −1.53726 −0.768630 0.639693i \(-0.779061\pi\)
−0.768630 + 0.639693i \(0.779061\pi\)
\(384\) 0 0
\(385\) −2.34213 −0.119366
\(386\) 0 0
\(387\) −18.0292 −0.916476
\(388\) 0 0
\(389\) −22.4816 −1.13986 −0.569930 0.821693i \(-0.693030\pi\)
−0.569930 + 0.821693i \(0.693030\pi\)
\(390\) 0 0
\(391\) −2.97441 −0.150422
\(392\) 0 0
\(393\) 41.1776 2.07713
\(394\) 0 0
\(395\) −6.18911 −0.311408
\(396\) 0 0
\(397\) −15.0925 −0.757469 −0.378734 0.925505i \(-0.623641\pi\)
−0.378734 + 0.925505i \(0.623641\pi\)
\(398\) 0 0
\(399\) 3.07701 0.154043
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −8.76014 −0.436374
\(404\) 0 0
\(405\) 10.4596 0.519742
\(406\) 0 0
\(407\) −26.7017 −1.32355
\(408\) 0 0
\(409\) 14.9349 0.738483 0.369241 0.929334i \(-0.379618\pi\)
0.369241 + 0.929334i \(0.379618\pi\)
\(410\) 0 0
\(411\) 30.7496 1.51676
\(412\) 0 0
\(413\) 4.40115 0.216566
\(414\) 0 0
\(415\) −16.0002 −0.785419
\(416\) 0 0
\(417\) 16.8992 0.827557
\(418\) 0 0
\(419\) −4.91475 −0.240101 −0.120051 0.992768i \(-0.538306\pi\)
−0.120051 + 0.992768i \(0.538306\pi\)
\(420\) 0 0
\(421\) −14.1682 −0.690516 −0.345258 0.938508i \(-0.612209\pi\)
−0.345258 + 0.938508i \(0.612209\pi\)
\(422\) 0 0
\(423\) −2.55531 −0.124243
\(424\) 0 0
\(425\) 3.21357 0.155881
\(426\) 0 0
\(427\) 2.21701 0.107289
\(428\) 0 0
\(429\) −14.9839 −0.723428
\(430\) 0 0
\(431\) −5.27141 −0.253915 −0.126957 0.991908i \(-0.540521\pi\)
−0.126957 + 0.991908i \(0.540521\pi\)
\(432\) 0 0
\(433\) 15.7421 0.756517 0.378259 0.925700i \(-0.376523\pi\)
0.378259 + 0.925700i \(0.376523\pi\)
\(434\) 0 0
\(435\) −3.36084 −0.161140
\(436\) 0 0
\(437\) 2.37852 0.113780
\(438\) 0 0
\(439\) −21.2511 −1.01426 −0.507129 0.861870i \(-0.669293\pi\)
−0.507129 + 0.861870i \(0.669293\pi\)
\(440\) 0 0
\(441\) −16.0877 −0.766082
\(442\) 0 0
\(443\) −20.6058 −0.979012 −0.489506 0.872000i \(-0.662823\pi\)
−0.489506 + 0.872000i \(0.662823\pi\)
\(444\) 0 0
\(445\) −13.5007 −0.639996
\(446\) 0 0
\(447\) −32.9435 −1.55817
\(448\) 0 0
\(449\) −28.0196 −1.32233 −0.661164 0.750241i \(-0.729937\pi\)
−0.661164 + 0.750241i \(0.729937\pi\)
\(450\) 0 0
\(451\) −40.9627 −1.92886
\(452\) 0 0
\(453\) 27.6038 1.29694
\(454\) 0 0
\(455\) −0.733188 −0.0343724
\(456\) 0 0
\(457\) −11.5111 −0.538466 −0.269233 0.963075i \(-0.586770\pi\)
−0.269233 + 0.963075i \(0.586770\pi\)
\(458\) 0 0
\(459\) 4.55778 0.212739
\(460\) 0 0
\(461\) −3.58908 −0.167160 −0.0835800 0.996501i \(-0.526635\pi\)
−0.0835800 + 0.996501i \(0.526635\pi\)
\(462\) 0 0
\(463\) −7.30656 −0.339565 −0.169782 0.985482i \(-0.554306\pi\)
−0.169782 + 0.985482i \(0.554306\pi\)
\(464\) 0 0
\(465\) −14.3064 −0.663444
\(466\) 0 0
\(467\) 42.6213 1.97228 0.986140 0.165918i \(-0.0530586\pi\)
0.986140 + 0.165918i \(0.0530586\pi\)
\(468\) 0 0
\(469\) −3.99976 −0.184692
\(470\) 0 0
\(471\) 1.64704 0.0758915
\(472\) 0 0
\(473\) −34.2676 −1.57563
\(474\) 0 0
\(475\) −2.56977 −0.117909
\(476\) 0 0
\(477\) 8.11611 0.371611
\(478\) 0 0
\(479\) −34.1882 −1.56210 −0.781049 0.624470i \(-0.785315\pi\)
−0.781049 + 0.624470i \(0.785315\pi\)
\(480\) 0 0
\(481\) −8.35879 −0.381128
\(482\) 0 0
\(483\) 1.10828 0.0504283
\(484\) 0 0
\(485\) −7.67511 −0.348509
\(486\) 0 0
\(487\) −25.6718 −1.16330 −0.581650 0.813439i \(-0.697593\pi\)
−0.581650 + 0.813439i \(0.697593\pi\)
\(488\) 0 0
\(489\) 40.0773 1.81236
\(490\) 0 0
\(491\) 11.7593 0.530690 0.265345 0.964153i \(-0.414514\pi\)
0.265345 + 0.964153i \(0.414514\pi\)
\(492\) 0 0
\(493\) −4.65243 −0.209535
\(494\) 0 0
\(495\) −10.8482 −0.487588
\(496\) 0 0
\(497\) 3.77444 0.169307
\(498\) 0 0
\(499\) 24.1953 1.08313 0.541566 0.840658i \(-0.317832\pi\)
0.541566 + 0.840658i \(0.317832\pi\)
\(500\) 0 0
\(501\) −20.4890 −0.915382
\(502\) 0 0
\(503\) 9.90898 0.441819 0.220910 0.975294i \(-0.429097\pi\)
0.220910 + 0.975294i \(0.429097\pi\)
\(504\) 0 0
\(505\) 15.5710 0.692902
\(506\) 0 0
\(507\) 25.4880 1.13196
\(508\) 0 0
\(509\) 31.1842 1.38221 0.691107 0.722753i \(-0.257123\pi\)
0.691107 + 0.722753i \(0.257123\pi\)
\(510\) 0 0
\(511\) 3.34373 0.147918
\(512\) 0 0
\(513\) −3.64469 −0.160917
\(514\) 0 0
\(515\) 3.28758 0.144868
\(516\) 0 0
\(517\) −4.85681 −0.213602
\(518\) 0 0
\(519\) −1.91237 −0.0839439
\(520\) 0 0
\(521\) −43.5489 −1.90791 −0.953955 0.299949i \(-0.903030\pi\)
−0.953955 + 0.299949i \(0.903030\pi\)
\(522\) 0 0
\(523\) −22.4814 −0.983044 −0.491522 0.870865i \(-0.663559\pi\)
−0.491522 + 0.870865i \(0.663559\pi\)
\(524\) 0 0
\(525\) −1.19739 −0.0522583
\(526\) 0 0
\(527\) −19.8044 −0.862695
\(528\) 0 0
\(529\) −22.1433 −0.962752
\(530\) 0 0
\(531\) 20.3850 0.884635
\(532\) 0 0
\(533\) −12.8231 −0.555431
\(534\) 0 0
\(535\) −3.65515 −0.158026
\(536\) 0 0
\(537\) 0.441095 0.0190346
\(538\) 0 0
\(539\) −30.5775 −1.31707
\(540\) 0 0
\(541\) −29.3186 −1.26051 −0.630253 0.776389i \(-0.717049\pi\)
−0.630253 + 0.776389i \(0.717049\pi\)
\(542\) 0 0
\(543\) 33.7979 1.45041
\(544\) 0 0
\(545\) 0.780421 0.0334295
\(546\) 0 0
\(547\) 38.1177 1.62980 0.814898 0.579604i \(-0.196793\pi\)
0.814898 + 0.579604i \(0.196793\pi\)
\(548\) 0 0
\(549\) 10.2686 0.438254
\(550\) 0 0
\(551\) 3.72037 0.158493
\(552\) 0 0
\(553\) 3.19233 0.135752
\(554\) 0 0
\(555\) −13.6509 −0.579450
\(556\) 0 0
\(557\) −0.325749 −0.0138024 −0.00690120 0.999976i \(-0.502197\pi\)
−0.00690120 + 0.999976i \(0.502197\pi\)
\(558\) 0 0
\(559\) −10.7273 −0.453715
\(560\) 0 0
\(561\) −33.8747 −1.43019
\(562\) 0 0
\(563\) 35.3560 1.49008 0.745040 0.667020i \(-0.232431\pi\)
0.745040 + 0.667020i \(0.232431\pi\)
\(564\) 0 0
\(565\) 3.57304 0.150319
\(566\) 0 0
\(567\) −5.39503 −0.226570
\(568\) 0 0
\(569\) 14.1728 0.594157 0.297078 0.954853i \(-0.403988\pi\)
0.297078 + 0.954853i \(0.403988\pi\)
\(570\) 0 0
\(571\) −8.26903 −0.346048 −0.173024 0.984918i \(-0.555354\pi\)
−0.173024 + 0.984918i \(0.555354\pi\)
\(572\) 0 0
\(573\) 50.8588 2.12465
\(574\) 0 0
\(575\) −0.925577 −0.0385992
\(576\) 0 0
\(577\) 10.4121 0.433462 0.216731 0.976231i \(-0.430461\pi\)
0.216731 + 0.976231i \(0.430461\pi\)
\(578\) 0 0
\(579\) 14.3559 0.596612
\(580\) 0 0
\(581\) 8.25286 0.342386
\(582\) 0 0
\(583\) 15.4261 0.638883
\(584\) 0 0
\(585\) −3.39595 −0.140405
\(586\) 0 0
\(587\) 35.3519 1.45913 0.729564 0.683912i \(-0.239723\pi\)
0.729564 + 0.683912i \(0.239723\pi\)
\(588\) 0 0
\(589\) 15.8369 0.652547
\(590\) 0 0
\(591\) 40.4520 1.66397
\(592\) 0 0
\(593\) −26.6716 −1.09527 −0.547636 0.836717i \(-0.684472\pi\)
−0.547636 + 0.836717i \(0.684472\pi\)
\(594\) 0 0
\(595\) −1.65755 −0.0679530
\(596\) 0 0
\(597\) 33.0568 1.35292
\(598\) 0 0
\(599\) −38.1497 −1.55876 −0.779378 0.626554i \(-0.784465\pi\)
−0.779378 + 0.626554i \(0.784465\pi\)
\(600\) 0 0
\(601\) −37.2826 −1.52079 −0.760395 0.649461i \(-0.774995\pi\)
−0.760395 + 0.649461i \(0.774995\pi\)
\(602\) 0 0
\(603\) −18.5259 −0.754434
\(604\) 0 0
\(605\) −9.61879 −0.391059
\(606\) 0 0
\(607\) −13.3600 −0.542266 −0.271133 0.962542i \(-0.587398\pi\)
−0.271133 + 0.962542i \(0.587398\pi\)
\(608\) 0 0
\(609\) 1.73351 0.0702454
\(610\) 0 0
\(611\) −1.52039 −0.0615085
\(612\) 0 0
\(613\) −26.5021 −1.07041 −0.535205 0.844722i \(-0.679766\pi\)
−0.535205 + 0.844722i \(0.679766\pi\)
\(614\) 0 0
\(615\) −20.9418 −0.844453
\(616\) 0 0
\(617\) 18.6828 0.752142 0.376071 0.926591i \(-0.377275\pi\)
0.376071 + 0.926591i \(0.377275\pi\)
\(618\) 0 0
\(619\) 23.4388 0.942083 0.471042 0.882111i \(-0.343878\pi\)
0.471042 + 0.882111i \(0.343878\pi\)
\(620\) 0 0
\(621\) −1.31274 −0.0526784
\(622\) 0 0
\(623\) 6.96364 0.278992
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 27.0883 1.08180
\(628\) 0 0
\(629\) −18.8971 −0.753476
\(630\) 0 0
\(631\) −23.8401 −0.949061 −0.474530 0.880239i \(-0.657382\pi\)
−0.474530 + 0.880239i \(0.657382\pi\)
\(632\) 0 0
\(633\) −50.9004 −2.02311
\(634\) 0 0
\(635\) −16.3561 −0.649070
\(636\) 0 0
\(637\) −9.57209 −0.379260
\(638\) 0 0
\(639\) 17.4822 0.691587
\(640\) 0 0
\(641\) −27.4559 −1.08444 −0.542221 0.840236i \(-0.682416\pi\)
−0.542221 + 0.840236i \(0.682416\pi\)
\(642\) 0 0
\(643\) −27.7027 −1.09249 −0.546245 0.837626i \(-0.683943\pi\)
−0.546245 + 0.837626i \(0.683943\pi\)
\(644\) 0 0
\(645\) −17.5190 −0.689808
\(646\) 0 0
\(647\) −3.42407 −0.134614 −0.0673070 0.997732i \(-0.521441\pi\)
−0.0673070 + 0.997732i \(0.521441\pi\)
\(648\) 0 0
\(649\) 38.7453 1.52088
\(650\) 0 0
\(651\) 7.37920 0.289214
\(652\) 0 0
\(653\) 32.5176 1.27251 0.636255 0.771478i \(-0.280482\pi\)
0.636255 + 0.771478i \(0.280482\pi\)
\(654\) 0 0
\(655\) 17.7380 0.693082
\(656\) 0 0
\(657\) 15.4873 0.604219
\(658\) 0 0
\(659\) 34.5960 1.34767 0.673834 0.738882i \(-0.264646\pi\)
0.673834 + 0.738882i \(0.264646\pi\)
\(660\) 0 0
\(661\) −2.35365 −0.0915465 −0.0457732 0.998952i \(-0.514575\pi\)
−0.0457732 + 0.998952i \(0.514575\pi\)
\(662\) 0 0
\(663\) −10.6043 −0.411835
\(664\) 0 0
\(665\) 1.32548 0.0514000
\(666\) 0 0
\(667\) 1.34000 0.0518849
\(668\) 0 0
\(669\) −17.6622 −0.682859
\(670\) 0 0
\(671\) 19.5173 0.753457
\(672\) 0 0
\(673\) −23.6612 −0.912071 −0.456035 0.889962i \(-0.650731\pi\)
−0.456035 + 0.889962i \(0.650731\pi\)
\(674\) 0 0
\(675\) 1.41829 0.0545901
\(676\) 0 0
\(677\) 16.3029 0.626572 0.313286 0.949659i \(-0.398570\pi\)
0.313286 + 0.949659i \(0.398570\pi\)
\(678\) 0 0
\(679\) 3.95880 0.151925
\(680\) 0 0
\(681\) 1.24474 0.0476986
\(682\) 0 0
\(683\) 3.14519 0.120347 0.0601737 0.998188i \(-0.480835\pi\)
0.0601737 + 0.998188i \(0.480835\pi\)
\(684\) 0 0
\(685\) 13.2460 0.506102
\(686\) 0 0
\(687\) −37.5385 −1.43218
\(688\) 0 0
\(689\) 4.82903 0.183972
\(690\) 0 0
\(691\) −3.58626 −0.136428 −0.0682139 0.997671i \(-0.521730\pi\)
−0.0682139 + 0.997671i \(0.521730\pi\)
\(692\) 0 0
\(693\) 5.59545 0.212553
\(694\) 0 0
\(695\) 7.27964 0.276133
\(696\) 0 0
\(697\) −28.9898 −1.09807
\(698\) 0 0
\(699\) −22.2733 −0.842455
\(700\) 0 0
\(701\) −14.8783 −0.561945 −0.280972 0.959716i \(-0.590657\pi\)
−0.280972 + 0.959716i \(0.590657\pi\)
\(702\) 0 0
\(703\) 15.1113 0.569933
\(704\) 0 0
\(705\) −2.48299 −0.0935149
\(706\) 0 0
\(707\) −8.03150 −0.302056
\(708\) 0 0
\(709\) 4.46752 0.167781 0.0838906 0.996475i \(-0.473265\pi\)
0.0838906 + 0.996475i \(0.473265\pi\)
\(710\) 0 0
\(711\) 14.7861 0.554521
\(712\) 0 0
\(713\) 5.70410 0.213620
\(714\) 0 0
\(715\) −6.45458 −0.241388
\(716\) 0 0
\(717\) −58.4299 −2.18210
\(718\) 0 0
\(719\) 8.85410 0.330202 0.165101 0.986277i \(-0.447205\pi\)
0.165101 + 0.986277i \(0.447205\pi\)
\(720\) 0 0
\(721\) −1.69572 −0.0631520
\(722\) 0 0
\(723\) 26.5455 0.987237
\(724\) 0 0
\(725\) −1.44774 −0.0537678
\(726\) 0 0
\(727\) 25.5022 0.945823 0.472912 0.881110i \(-0.343203\pi\)
0.472912 + 0.881110i \(0.343203\pi\)
\(728\) 0 0
\(729\) −15.1110 −0.559668
\(730\) 0 0
\(731\) −24.2516 −0.896978
\(732\) 0 0
\(733\) 36.2118 1.33751 0.668756 0.743482i \(-0.266827\pi\)
0.668756 + 0.743482i \(0.266827\pi\)
\(734\) 0 0
\(735\) −15.6324 −0.576610
\(736\) 0 0
\(737\) −35.2117 −1.29704
\(738\) 0 0
\(739\) −15.4633 −0.568825 −0.284413 0.958702i \(-0.591799\pi\)
−0.284413 + 0.958702i \(0.591799\pi\)
\(740\) 0 0
\(741\) 8.47983 0.311514
\(742\) 0 0
\(743\) −49.2279 −1.80600 −0.902998 0.429645i \(-0.858639\pi\)
−0.902998 + 0.429645i \(0.858639\pi\)
\(744\) 0 0
\(745\) −14.1910 −0.519919
\(746\) 0 0
\(747\) 38.2252 1.39859
\(748\) 0 0
\(749\) 1.88532 0.0688880
\(750\) 0 0
\(751\) 34.7967 1.26975 0.634875 0.772615i \(-0.281052\pi\)
0.634875 + 0.772615i \(0.281052\pi\)
\(752\) 0 0
\(753\) 25.7199 0.937286
\(754\) 0 0
\(755\) 11.8909 0.432753
\(756\) 0 0
\(757\) −38.0393 −1.38256 −0.691282 0.722585i \(-0.742954\pi\)
−0.691282 + 0.722585i \(0.742954\pi\)
\(758\) 0 0
\(759\) 9.75664 0.354144
\(760\) 0 0
\(761\) −13.8507 −0.502088 −0.251044 0.967976i \(-0.580774\pi\)
−0.251044 + 0.967976i \(0.580774\pi\)
\(762\) 0 0
\(763\) −0.402539 −0.0145729
\(764\) 0 0
\(765\) −7.67737 −0.277576
\(766\) 0 0
\(767\) 12.1290 0.437951
\(768\) 0 0
\(769\) −7.18816 −0.259212 −0.129606 0.991566i \(-0.541371\pi\)
−0.129606 + 0.991566i \(0.541371\pi\)
\(770\) 0 0
\(771\) 22.8038 0.821258
\(772\) 0 0
\(773\) −31.7005 −1.14019 −0.570093 0.821580i \(-0.693093\pi\)
−0.570093 + 0.821580i \(0.693093\pi\)
\(774\) 0 0
\(775\) −6.16275 −0.221373
\(776\) 0 0
\(777\) 7.04112 0.252599
\(778\) 0 0
\(779\) 23.1821 0.830583
\(780\) 0 0
\(781\) 33.2280 1.18899
\(782\) 0 0
\(783\) −2.05332 −0.0733798
\(784\) 0 0
\(785\) 0.709493 0.0253229
\(786\) 0 0
\(787\) 52.0064 1.85383 0.926915 0.375273i \(-0.122451\pi\)
0.926915 + 0.375273i \(0.122451\pi\)
\(788\) 0 0
\(789\) −20.9226 −0.744866
\(790\) 0 0
\(791\) −1.84296 −0.0655282
\(792\) 0 0
\(793\) 6.10977 0.216964
\(794\) 0 0
\(795\) 7.88642 0.279702
\(796\) 0 0
\(797\) 0.650091 0.0230274 0.0115137 0.999934i \(-0.496335\pi\)
0.0115137 + 0.999934i \(0.496335\pi\)
\(798\) 0 0
\(799\) −3.43722 −0.121600
\(800\) 0 0
\(801\) 32.2539 1.13963
\(802\) 0 0
\(803\) 29.4364 1.03879
\(804\) 0 0
\(805\) 0.477410 0.0168265
\(806\) 0 0
\(807\) 72.9438 2.56774
\(808\) 0 0
\(809\) −0.529620 −0.0186205 −0.00931023 0.999957i \(-0.502964\pi\)
−0.00931023 + 0.999957i \(0.502964\pi\)
\(810\) 0 0
\(811\) 4.69632 0.164910 0.0824551 0.996595i \(-0.473724\pi\)
0.0824551 + 0.996595i \(0.473724\pi\)
\(812\) 0 0
\(813\) 25.0115 0.877191
\(814\) 0 0
\(815\) 17.2640 0.604733
\(816\) 0 0
\(817\) 19.3931 0.678478
\(818\) 0 0
\(819\) 1.75162 0.0612065
\(820\) 0 0
\(821\) 17.7904 0.620889 0.310445 0.950591i \(-0.399522\pi\)
0.310445 + 0.950591i \(0.399522\pi\)
\(822\) 0 0
\(823\) 25.4813 0.888221 0.444111 0.895972i \(-0.353520\pi\)
0.444111 + 0.895972i \(0.353520\pi\)
\(824\) 0 0
\(825\) −10.5411 −0.366995
\(826\) 0 0
\(827\) −11.3759 −0.395580 −0.197790 0.980244i \(-0.563376\pi\)
−0.197790 + 0.980244i \(0.563376\pi\)
\(828\) 0 0
\(829\) 9.15670 0.318025 0.159013 0.987277i \(-0.449169\pi\)
0.159013 + 0.987277i \(0.449169\pi\)
\(830\) 0 0
\(831\) −71.1687 −2.46881
\(832\) 0 0
\(833\) −21.6400 −0.749783
\(834\) 0 0
\(835\) −8.82603 −0.305437
\(836\) 0 0
\(837\) −8.74058 −0.302119
\(838\) 0 0
\(839\) −41.3930 −1.42904 −0.714522 0.699613i \(-0.753356\pi\)
−0.714522 + 0.699613i \(0.753356\pi\)
\(840\) 0 0
\(841\) −26.9040 −0.927726
\(842\) 0 0
\(843\) 21.8184 0.751464
\(844\) 0 0
\(845\) 10.9794 0.377704
\(846\) 0 0
\(847\) 4.96134 0.170474
\(848\) 0 0
\(849\) −42.9388 −1.47366
\(850\) 0 0
\(851\) 5.44277 0.186576
\(852\) 0 0
\(853\) −26.0489 −0.891896 −0.445948 0.895059i \(-0.647133\pi\)
−0.445948 + 0.895059i \(0.647133\pi\)
\(854\) 0 0
\(855\) 6.13930 0.209960
\(856\) 0 0
\(857\) −17.4390 −0.595706 −0.297853 0.954612i \(-0.596270\pi\)
−0.297853 + 0.954612i \(0.596270\pi\)
\(858\) 0 0
\(859\) 53.1349 1.81294 0.906470 0.422271i \(-0.138767\pi\)
0.906470 + 0.422271i \(0.138767\pi\)
\(860\) 0 0
\(861\) 10.8017 0.368121
\(862\) 0 0
\(863\) −1.21959 −0.0415152 −0.0207576 0.999785i \(-0.506608\pi\)
−0.0207576 + 0.999785i \(0.506608\pi\)
\(864\) 0 0
\(865\) −0.823790 −0.0280097
\(866\) 0 0
\(867\) 15.4908 0.526095
\(868\) 0 0
\(869\) 28.1035 0.953345
\(870\) 0 0
\(871\) −11.0228 −0.373493
\(872\) 0 0
\(873\) 18.3362 0.620585
\(874\) 0 0
\(875\) −0.515797 −0.0174371
\(876\) 0 0
\(877\) −58.3629 −1.97077 −0.985387 0.170331i \(-0.945516\pi\)
−0.985387 + 0.170331i \(0.945516\pi\)
\(878\) 0 0
\(879\) 24.1315 0.813935
\(880\) 0 0
\(881\) −24.5870 −0.828357 −0.414178 0.910196i \(-0.635931\pi\)
−0.414178 + 0.910196i \(0.635931\pi\)
\(882\) 0 0
\(883\) −31.9454 −1.07505 −0.537525 0.843248i \(-0.680641\pi\)
−0.537525 + 0.843248i \(0.680641\pi\)
\(884\) 0 0
\(885\) 19.8081 0.665842
\(886\) 0 0
\(887\) 27.0532 0.908359 0.454179 0.890910i \(-0.349933\pi\)
0.454179 + 0.890910i \(0.349933\pi\)
\(888\) 0 0
\(889\) 8.43641 0.282948
\(890\) 0 0
\(891\) −47.4949 −1.59114
\(892\) 0 0
\(893\) 2.74861 0.0919789
\(894\) 0 0
\(895\) 0.190010 0.00635132
\(896\) 0 0
\(897\) 3.05425 0.101979
\(898\) 0 0
\(899\) 8.92208 0.297568
\(900\) 0 0
\(901\) 10.9172 0.363705
\(902\) 0 0
\(903\) 9.03623 0.300707
\(904\) 0 0
\(905\) 14.5591 0.483960
\(906\) 0 0
\(907\) 1.34778 0.0447524 0.0223762 0.999750i \(-0.492877\pi\)
0.0223762 + 0.999750i \(0.492877\pi\)
\(908\) 0 0
\(909\) −37.1999 −1.23384
\(910\) 0 0
\(911\) −54.8993 −1.81890 −0.909448 0.415818i \(-0.863495\pi\)
−0.909448 + 0.415818i \(0.863495\pi\)
\(912\) 0 0
\(913\) 72.6535 2.40448
\(914\) 0 0
\(915\) 9.97801 0.329863
\(916\) 0 0
\(917\) −9.14922 −0.302134
\(918\) 0 0
\(919\) 9.58092 0.316045 0.158023 0.987435i \(-0.449488\pi\)
0.158023 + 0.987435i \(0.449488\pi\)
\(920\) 0 0
\(921\) −50.3468 −1.65898
\(922\) 0 0
\(923\) 10.4018 0.342380
\(924\) 0 0
\(925\) −5.88040 −0.193346
\(926\) 0 0
\(927\) −7.85416 −0.257965
\(928\) 0 0
\(929\) −10.5310 −0.345512 −0.172756 0.984965i \(-0.555267\pi\)
−0.172756 + 0.984965i \(0.555267\pi\)
\(930\) 0 0
\(931\) 17.3047 0.567139
\(932\) 0 0
\(933\) −36.6458 −1.19973
\(934\) 0 0
\(935\) −14.5922 −0.477215
\(936\) 0 0
\(937\) −4.05730 −0.132546 −0.0662731 0.997802i \(-0.521111\pi\)
−0.0662731 + 0.997802i \(0.521111\pi\)
\(938\) 0 0
\(939\) −32.2878 −1.05367
\(940\) 0 0
\(941\) −14.4347 −0.470558 −0.235279 0.971928i \(-0.575600\pi\)
−0.235279 + 0.971928i \(0.575600\pi\)
\(942\) 0 0
\(943\) 8.34969 0.271903
\(944\) 0 0
\(945\) −0.731551 −0.0237974
\(946\) 0 0
\(947\) −60.1369 −1.95419 −0.977094 0.212810i \(-0.931739\pi\)
−0.977094 + 0.212810i \(0.931739\pi\)
\(948\) 0 0
\(949\) 9.21487 0.299127
\(950\) 0 0
\(951\) 10.5114 0.340857
\(952\) 0 0
\(953\) −39.8898 −1.29216 −0.646078 0.763271i \(-0.723592\pi\)
−0.646078 + 0.763271i \(0.723592\pi\)
\(954\) 0 0
\(955\) 21.9084 0.708938
\(956\) 0 0
\(957\) 15.2609 0.493313
\(958\) 0 0
\(959\) −6.83223 −0.220624
\(960\) 0 0
\(961\) 6.97950 0.225145
\(962\) 0 0
\(963\) 8.73232 0.281395
\(964\) 0 0
\(965\) 6.18409 0.199073
\(966\) 0 0
\(967\) −22.2323 −0.714942 −0.357471 0.933924i \(-0.616361\pi\)
−0.357471 + 0.933924i \(0.616361\pi\)
\(968\) 0 0
\(969\) 19.1707 0.615852
\(970\) 0 0
\(971\) −7.27517 −0.233471 −0.116736 0.993163i \(-0.537243\pi\)
−0.116736 + 0.993163i \(0.537243\pi\)
\(972\) 0 0
\(973\) −3.75482 −0.120374
\(974\) 0 0
\(975\) −3.29984 −0.105679
\(976\) 0 0
\(977\) −41.3326 −1.32235 −0.661173 0.750233i \(-0.729941\pi\)
−0.661173 + 0.750233i \(0.729941\pi\)
\(978\) 0 0
\(979\) 61.3040 1.95929
\(980\) 0 0
\(981\) −1.86446 −0.0595276
\(982\) 0 0
\(983\) 3.54531 0.113078 0.0565389 0.998400i \(-0.481993\pi\)
0.0565389 + 0.998400i \(0.481993\pi\)
\(984\) 0 0
\(985\) 17.4254 0.555221
\(986\) 0 0
\(987\) 1.28072 0.0407658
\(988\) 0 0
\(989\) 6.98498 0.222109
\(990\) 0 0
\(991\) 57.4573 1.82519 0.912596 0.408863i \(-0.134075\pi\)
0.912596 + 0.408863i \(0.134075\pi\)
\(992\) 0 0
\(993\) 67.2899 2.13538
\(994\) 0 0
\(995\) 14.2398 0.451433
\(996\) 0 0
\(997\) −43.2684 −1.37032 −0.685162 0.728391i \(-0.740268\pi\)
−0.685162 + 0.728391i \(0.740268\pi\)
\(998\) 0 0
\(999\) −8.34013 −0.263870
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))